Invertibility of Multidimensional Integral Operators with Bihomogeneous Kernels

Mathematical Notes -     

Chemical versus Electrochemical Synthesis of Carbon Nano‐onion/Polypyrrole Composites for Supercapacitor Electrodes

The development of high‐surface‐area carbon electrodes with a defined pore size distribution and the incorporation of pseudo‐active materials to optimize the overall capacitance and conductivity without destroying the stability are at present important research areas. Composite electrodes of carbon nano‐onions (CNOs) and polypyrrole (Ppy) were fabricated to improve the specific capacitance of a supercapacitor. The carbon nanostructures were uniformly coated with Ppy by chemical polymerization or by electrochemical potentiostatic deposition to form homogenous composites or bilayers. The materials were characterized by transmission‐ and scanning electron microscopy, differential thermogravimetric analyses, FTIR spectroscopy, piezoelectric microgravimetry, and cyclic voltammetry. The composites show higher mechanical and electrochemical stabilities, with high specific capacitances of up to about 800 F g^?1 for the CNOs/SDS/Ppy composites (chemical synthesis) and about 1300 F g^?1 for the CNOs/Ppy bilayer (electrochemical deposition).     

Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

Synthesis and luminescence properties of hybrid systems based on liquid crystal terbium(ІІІ) and europium(ІІІ) complexes

Russian Journal of General Chemistry - Hybrid liquid crystal systems with different ratios of the components have been prepared on the basis of 5,5′-di(heptadecyl)-2,2′-bipyridine...     

Synthesis of Highly Substituted γ‐Butyrolactones by a Gold‐Catalyzed Cascade Reaction of Benzyl Esters

Easily accessible benzylic esters of 3‐butynoic acids in a gold‐catalyzed cyclization/rearrangement cascade reaction provided 3‐propargyl γ‐butyrolactones with the alkene and the carbonyl group not being conjugated. Crossover experiments showed that the formation of the new C?C bond is an intermolecular process. Initially propargylic–benzylic esters were used, but alkyl‐substituted benzylic esters worked equally well. In the case of the propargylic–benzylic products, a simple treatment of the products with aluminum oxide initiated a twofold tautomerization to the allenyl‐substituted γ‐butyrolactones with conjugation of the carbonyl group, the olefin, and the allene. The synthetic sequence can be conducted stepwise or as a one‐pot cascade reaction with similar yields. Even in the presence of the gold catalyst the new allene remains intact.     

Unfamiliar Aspects of Bäcklund Transformations and an Associated Degasperis–Procesi Equation

We summarize the results of our recent work on Bäcklund transformations (BTs), particularly focusing on the relation between BTs and infinitesimal symmetries. We present a BT for an associated Degasperis–Procesi (aDP) equation and its superposition principle and investigate the solutions generated by applying this BT. Following our general methodology, we use the superposition principle of the BT to generate the infinitesimal symmetries of the aDP equation.     

Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

Triesterase and Promiscuous Diesterase Activities of a Di‐CoII‐Containing Organophosphate Degrading Enzyme Reaction Mechanisms

The reaction mechanism for the hydrolysis of trimethyl phosphate and of the obtained phosphodiester by the di‐Co^II derivative of organophosphate degrading enzyme from Agrobacterium radiobacter P230(OpdA), have been investigated at density functional level of theory in the framework of the cluster model approach. Both mechanisms proceed by a multistep sequence and each catalytic cycle begins with the nucleophilic attack by a metal‐bound hydroxide on the phosphorus atom of the substrate, leading to the cleavage of the phosphate‐ester bond. Four exchange‐correlation functionals were used to derive the potential energy profiles in protein environments. Although the enzyme is confirmed to work better as triesterase, as revealed by the barrier heights in the rate‐limiting steps of the catalytic processes, its promiscuous ability to hydrolyze also the product of the reaction has been confirmed. The important role played by water molecules and some residues in the outer coordination sphere has been elucidated, while the binuclear Co^II center accomplishes both structural and catalytic functions. To correctly describe the electronic configuration of the d shell of the metal ions, high‐ and low‐spin arrangement jointly with the occurrence of antiferromagnetic coupling, have been herein considered.